Purity of reciprocity sheaves

Abstract

The purpose of this paper is to prove a conjecture on reciprocity sheaves by Kahn-Saito-Yamazaki. This is accomplished by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalizations, reciprocity sheaves and cube-invariant sheaves in the context of theory of modulus (pre)sheave with transfers. The main results of this paper is expected to play a crucial role in deducing the main properties of the triangulated category of motives with modulus, which is a new triangulated category enlarging Voevodsky's triangulated category of motives to encompass non homotopy invariant motivic phenomena.

A mistake in theory of modulus sheave with transfers (pointed by Ayoub) has been repaired

Cited by in corpus (3)

• Gysin triangles in the category of motifs with modulus
• A remark on the tensor product of SC-reciprocity sheaves
• Semi-purity for cycles with modulus